Theorems · Theorem · Lie groups
IsTopologicalAddGroup.exist_openNormalAddSubgroup_sub_clopen_nhds_of_zero
∀ {G : Type u_1} [inst : AddGroup G] [inst_1 : TopologicalSpace G] [IsTopologicalAddGroup G] [CompactSpace G]
{W : Set G}, IsClopen W → 0 ∈ W → ∃ H, ↑H ⊆ W- Defined in
- Mathlib.Topology.Algebra.ClopenNhdofOne
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- SetLike.coestatement and proof · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupproof · cited by 3,232
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- CompactSpacestatement and proof · cited by 593
- IsClopenstatement and proof · cited by 189
- AddSubgroup.FiniteIndexproof · cited by 66
- OpenAddSubgroupproof · cited by 47
- OpenAddSubgroup.toAddSubgroupproof · cited by 27
- OpenNormalAddSubgroupstatement · cited by 20
Cited by1
Results whose statement or proof uses this declaration.
- ProfiniteGrp.exist_openNormalAddSubgroup_sub_open_nhds_of_zeroproof · cited by 2